Extending economic design of p charts to handle user specified constraints using a genetic algorithm

Abstract

For certain processes, the quality of the output can be monitored using attribute inspection statistical process control. Various approaches have been used to determine optimal or near-optimal parameters for such a plan. Since most of these approaches use an unconstrained model, some solutions can result in theoretical and pragmatic problems. In this paper we used Duncan's loss function as the objective function for the development of a Genetic Algorithm (GA). In addition to formulating a GA to find a solution to the model, user constraints concerning the frequency of inspection, the number of defects allowed and the production rate are used to limit the search space for the GA. The GA is selected over other search techniques such as traditional calculus-based, enumeration, or undirected random search methods because the GA is more robust than other search techniques.

Notes

*Loss function values developed by our variation of Duncan's loss function resulted in a slightly different value than reported by Duncan (1978). This is likely due to rounding differences in the processors used to calculate the loss.

*Loss function values developed by our variation of Duncan's loss function resulted in a slightly different value than reported by Duncan (1978). This is likely due to rounding differences in the processors used to calculate the loss.

*Loss function values developed by our variation of Duncan's loss function resulted in a slightly different value than reported by Duncan (1978). This is likely due to rounding differences in the processors used to calculate the loss.

^†Deceased